4. Discussion 
The startling variety of suggestions concerning the width of the "fertile window" found in the literature depends in part from conceptual approaches adopted. To try and measure the window summing lifetime of sperm and ovum less the time needed for capacitation of spermatozoa is a deductive theoretical solution. But when, instead of a single cycle, a mixture of cycles of a group of women is considered, due account has to be taken of the biological variability of both patterns and its interaction. When trying to make evaluations starting from aggregates of distinct empirical experiences, one should be sure that the single cases record real facts uniformly and homogeneously, without the impact of confounding factors. According to Potter and Millmann [Potter and Millman 1985], the lines of research followed to clarify the point can be grouped into two categories. In the first one, assumptions are made on mean fecundability and average coital pattern: a chosen model allows us to estimate the length of the fertile period assuring compatibility between the two. In the second, starting from estimated daily probabilities, given a certain coital pattern, the fecundability in a cycle is derived. The procedure followed in this exercise falls into this second class. That is, it starts from and deals with aggregations of distinct ascertained facts. One aspect of the documentation that has been collected needs to be stressed here: that is, its reliability about type and timing of what is essential for the study of fecundability, the acts of intercourse. This has been assured by the long experience of the cooperating centres, an agreed rigorous protocol, the follow up of the ongoing work through periodical meetings of the Principal Investigators, the scrupulous screening of the forms arriving at the coordinating centre. At the same time, the main weakness of the information has to be underlined: the reliance on the surrogate indicators of the true day of ovulation, the BBT shift and the peak mucus day. The distribution of deviations between these markers and the true ovulation day is poorly known (see, e.g. [Hilgers, Abraham, and Cavanagh 1978, Hilgers and Bailey 1980, France 1982, Guida et al 1999]). Several recent studies have obtained estimates of error in BBT reference day. There have been small validation studies and Dunson et al. [Dunson et al 1999] present estimates. These studies suggest that most cycles have errors of less than _ one day. A major challenge is to try to obtain correct measures of daily fecundability, possibly using the methods of Dunson and Weinberg [Dunson and Weinberg 2000] and Dunson et al. [Dunson et al in press]. Furthermore, while ovulation is practically instantaneous, we have only information on the level of days. The Schwartz et al. [Schwartz, MacDonald, and Heuchel 1980] model (see [2.5.1]) chosen has its merits: it rests on appealing biological hypotheses, and in general fits well the data. But it has weaknesses: it is based on rather simplistic assumptions; with high frequency of intercourse it tends to underestimate observed fecundability; the parameter k, supposed to measure the socalled cycle viability, is not independent from the pattern of intercourse episodes. But it is not the place, here, to enter into a thorough discussion of comparative evaluation of advantages and disadvantages of different proposed or conceivable models, or of other approaches to the desired estimation. These words of caution do not detract significance for applications from the main results of the study in the area of fertility regulation. Couples attempting pregnancy should maximise their intercourse frequency during the four days preceding the first upward shift of the basal body temperature or the peak mucus day. In both distinct sets of cycles the maximum level of conception probabilities is achieved in the second day before the reference point: 0.255 in the window around BBT reference day and 0.203 in the other case. Couples wanting to avoid pregnancy are informed that the unsafe period might be extended up to 1112 days. The computed confidence intervals may help to qualify the situation obtaining at the two extremes of the window, where the probabilities of conception are very low. In both sets, eight days before the reference point the estimated probability is 0.003, which means, approximately, a pregnancy every 26 years: but the computed upper confidence limits reach 0.011. Obviously, these conclusions are drawn from a posteriori observation, but concerning the determination of the beginning of the premenstrual infertile phase they provide sufficient information. For other purposes, needing day to day decisions, apart from some observations currently possible  as a first evidence of the mucus symptom , it would be advantageous to be able to make reliable forecasts. For this sake, an improvement of usual calendar methods through a sequential procedure using updated accumulated observations made on preceding cycles might prove useful. The results obtained are of interest also from a demographic point of view. Contraception has an obvious impact as a confounding factor on the link between socalled natural and actual fertility of a population. The said results make clear how behaviour together with physiology has an influence on natural fertility. What matters is not only frequency of coitions, but also their allocation to the different days of the fertile interval. The maximum daily fecundability estimated in the BBT window is .255 (Table 9) which corresponds to an average number of 3.92 cycles needed for obtaining a pregnancy, while after one year (roughly 13 cycles) 2.2% subjects remain without success. Couples with at least three acts of intercourse in the same window roughly representing those attempting a pregnancy reach a proportion of .227 conception cycles on the whole. This corresponds to 4.41 cycles for a pregnancy and 3.5% of failures in a year. After the elaboration for the whole data set, some covariates are taken into consideration, one by one: centres, reproductive history and age of the women, and previous use of oral contraception. Homogeneity was observed among three sets of European populations both in pattern and level of conception probabilities and in the extension of the fertile window. Auckland shows the same pattern but a significantly higher level of probabilities. Similar results are reached in the other elaboration on the European set, with a clear difference in the level of daily fecundability only according to previous reproductive experience. Attention should be drawn, however, on the upper age limit of 40 years for the women, the lack of standardisation with respect to the reproductive history of the woman and the decline of k with increasing age. The interrelations between covariates for instance between age and reproductive history of the women show that for the distinct evaluation of the impact of various factors, a multivariate analysis approach is needed. A consideration of heterogeneity between units due to unobservable phenomena has to be added to this. The study design is rather complex, hierarchical and multilevel. Considering the women subjects, there are days in a cycle, cycles in a woman, women in a centre, various centres. At each level there is involvement of specific covariates and there is unobservable heterogeneity between the units. Furthermore, there is a confounding factor, the age of the partner. If one wants  particularly in view of more efficient applications in the field of fertility regulation  to try to make clusterization of subjects, the results by cycle shown in Figures 6 and 7 suggest that longitudinal analyses of consecutive cycles within women are needed to characterise them. Also, longitudinal analysis of cycles might prove useful in clarifying the impact of physiology and behaviour on the outcomes: a rather intriguing area of study since at every step the event number and allocation of acts of intercourse may change. These examples show that the database presented in this paper offers possibilities of investigation along several lines of research.


Daily Fecundability: First Results from a New Data Base Bernardo Colombo, Guido Masarotto © 2000 MaxPlanckGesellschaft ISSN 14359871 http://www.demographicresearch.org/Volumes/Vol3/5 